How can I add a vertex at the center of a circle?
If you've already added the circle there are some other fast ways to do this:
Method 1:

Select the circle.

Extrude (E), then cancel the translate part of the extrusion with Esc.

Press ⎇ AltM &gt; Center to merge the extruded vertices into a single central vertex.



Method 2:

Select the circle.

Fill (F) to make an n-gon.

Poke Faces (⎇ AltP) to triangulate the n-gon with a central vertex.